FEUCAT Mathematics — Arithmetic — Multiples, Factors, PEMDAS, Fractions & DecimalsMemory Anchors

Tags

• sequence
• process
• formula

Topic

Order of Operations

Concept

PEMDAS Order of Operations

Anchor Id

A1

Difficulty

easy

Memory Aid

Please Excuse My Dear Aunt Sally - Picture your favorite tita (aunt) serving you a meal in this exact order: Parentheses (she serves soup in bowls first), Exponents (she adds extra rice on top), Multiplication/Division (she multiplies the ulam portions and divides them equally), Addition/Subtraction (she adds more vegetables and removes what you don't like)

Anchor Type

mnemonic

Why It Works

Associates mathematical operations with a familiar family scenario that Filipino students experience regularly during meals

Example Usage

When solving 2 + 3 × 4², think 'Tita serves soup (parentheses) first, then extra rice (exponents: 4² = 16), then multiplies ulam (3 × 16 = 48), finally adds (2 + 48 = 50)'

Recall Trigger

Think of your tita serving food in order

Tags

• process
• analogy

Topic

GCF

Concept

Finding GCF using Prime Factorization

Anchor Id

A2

Difficulty

medium

Memory Aid

Finding GCF is like finding the common ingredients in your favorite adobo recipes from two different lolas. List all ingredients (prime factors) for each recipe, then keep only the common ones with the smallest amount used. For example, if Lola A uses 3 bay leaves and Lola B uses 2 bay leaves, you can only use 2 bay leaves in your combined recipe.

Anchor Type

analogy

Why It Works

Connects abstract math to familiar cooking scenarios, making the 'common factors' concept tangible

Example Usage

For GCF of 24 and 30: 24 = 2³×3, 30 = 2×3×5. Common ingredients are 2 and 3. Take the smallest amount: 2¹×3¹ = 6

Recall Trigger

Think of two lolas comparing their adobo ingredients

Tags

• process
• analogy

Topic

LCM

Concept

Finding LCM using Prime Factorization

Anchor Id

A3

Difficulty

medium

Memory Aid

Finding LCM is like planning a bayanihan (community work) where you need enough supplies for everyone. Take ALL different ingredients (prime factors) from both recipes, but use the LARGEST amount of each ingredient mentioned. If one recipe needs 3 bay leaves and another needs 2, bring 3 bay leaves to satisfy both.

Anchor Type

analogy

Why It Works

Uses the familiar concept of community preparation where you need maximum supplies

Example Usage

For LCM of 24 and 30: 24 = 2³×3, 30 = 2×3×5. Take maximum of each: 2³×3¹×5¹ = 8×3×5 = 120

Recall Trigger

Think of preparing supplies for bayanihan - take the maximum of each item

Tags

• definition
• classification

Topic

Prime and Composite Numbers

Concept

Prime vs Composite Numbers

Anchor Id

A4

Difficulty

easy

Memory Aid

In the Kingdom of Numbers, Prime numbers are like hermit crabs - they live alone and can only be divided by 1 and themselves. Composite numbers are like families in a bahay kubo - they have many divisors living together. The number 1 is the village chief who doesn't belong to either group, and 0 is the empty lot.

Anchor Type

micro_story

Why It Works

Creates a memorable visual story that clearly distinguishes between number types

Example Usage

When asked if 17 is prime, think: 'Is 17 a hermit crab? Yes, it only has factors 1 and 17, so it lives alone - it's prime!'

Recall Trigger

Picture the Kingdom of Numbers with hermit crabs and families

Tags

• rule
• process

Topic

Divisibility Rules

Concept

Divisibility Rule for 3

Anchor Id

A5

Difficulty

easy

Memory Aid

Add the digits, don't you wait, if the sum divides by three, then the number's really great! Like a jeepney route that's planned, where all passengers (digits) must add up to stations divisible by 3 to make the trip complete.

Anchor Type

rhyme

Why It Works

Rhythmic pattern makes the rule memorable and the jeepney analogy provides familiar context

Example Usage

For 243: 2+4+3 = 9, and 9÷3 = 3, so 243 is divisible by 3. Like counting 9 passengers on a jeepney!

Recall Trigger

Think of passengers boarding a jeepney - count them up

Tags

• process
• conversion

Topic

Fractions

Concept

Converting Mixed Numbers to Improper Fractions

Anchor Id

A6

Difficulty

medium

Memory Aid

MAD method: Multiply, Add, Drop! Picture a basketball player (the whole number) holding basketballs (numerator) while standing on a court divided into sections (denominator). To find total basketballs: Multiply player number × court sections, Add the basketballs he's already holding, Drop the answer over the same court sections.

Anchor Type

visual_association

Why It Works

Visual sports imagery makes the abstract process concrete and memorable

Example Usage

For 3²⁄₅: Player #3 on a 5-section court holding 2 balls. MAD: 3×5=15, 15+2=17, Drop over 5 = ¹⁷⁄₅

Recall Trigger

Picture a basketball player on a sectioned court

Tags

• process
• application

Topic

Adding Fractions

Concept

Adding Fractions with Different Denominators

Anchor Id

A7

Difficulty

medium

Memory Aid

Two sari-sari store owners want to combine their rice supplies. Owner A has ¾ sack, Owner B has ⅖ sack. But their sacks are different sizes! They must first find identical sacks (LCD) that both portions can fit into. ¾ becomes ¹⁵⁄₂₀ and ⅖ becomes ⁸⁄₂₀. Now they can add: 15 + 8 = 23 portions in 20-portion sacks = ²³⁄₂₀ sacks total.

Anchor Type

micro_story

Why It Works

Familiar business scenario makes the need for common denominators logical

Example Usage

For ¾ + ⅖: Find LCD (20), convert (¹⁵⁄₂₀ + ⁸⁄₂₀), add numerators (23), result = ²³⁄₂₀

Recall Trigger

Think of two store owners combining different-sized supplies

Tags

• process
• rule

Topic

Multiplying Fractions

Concept

Multiplying Fractions

Anchor Id

A8

Difficulty

easy

Memory Aid

FANT: Fraction multiplication is so FANTASTIC! Just multiply Across (numerators together, denominators together). No need for common denominators - it's like crossing the street straight across, not diagonally!

Anchor Type

acronym

Why It Works

Simple acronym with a clear visual of crossing straight across

Example Usage

For ²⁄₃ × ⁴⁄₅: Multiply across - (2×4)/(3×5) = ⁸⁄₁₅. Straight across like crossing the street!

Recall Trigger

Think FANT and crossing straight across the street

Tags

• process
• rule

Topic

Dividing Fractions

Concept

Dividing Fractions

Anchor Id

A9

Difficulty

medium

Memory Aid

Dividing fractions, here's the key - flip the second, then multiply! Like doing tinikling dance steps: when the second bamboo pole comes down, you flip it up and step-step (multiply) through!

Anchor Type

rhyme

Why It Works

Traditional Filipino dance provides memorable physical action for the flip-and-multiply rule

Example Usage

For ³⁄₄ ÷ ²⁄₅: Flip the second (²⁄₅ becomes ⁵⁄₂), then multiply: ³⁄₄ × ⁵⁄₂ = ¹⁵⁄₈

Recall Trigger

Think of flipping bamboo poles in tinikling dance

Tags

• place value
• visual

Topic

Decimals

Concept

Decimal Place Values

Anchor Id

A10

Difficulty

easy

Memory Aid

Think of the decimal point as the Rizal Monument in Luneta. To the left (west) are the whole number provinces: ones, tens, hundreds. To the right (east) are the decimal barangays: tenths, hundredths, thousandths. The farther you go from the monument, the smaller/larger the place value becomes.

Anchor Type

visual_association

Why It Works

Uses familiar Manila landmark to create spatial memory for place values

Example Usage

In 423.567, the 5 is in the first barangay east of Rizal (tenths place), worth 5/10 = 0.5

Recall Trigger

Picture Rizal Monument with provinces on left, barangays on right

Tags

• conversion
• process

Topic

Converting Fractions to Decimals

Concept

Converting Fractions to Decimals

Anchor Id

A11

Difficulty

medium

Memory Aid

Journey through your house: Start at the door (fraction), walk to the kitchen (divide numerator by denominator), cook using long division, serve the decimal result on a plate. If the division doesn't end, you have a repeating decimal - like a broken record player in your living room.

Anchor Type

method_of_loci

Why It Works

Creates a memorable journey through familiar spaces with clear action steps

Example Usage

For ³⁄₈: Door (³⁄₈) → Kitchen (3 ÷ 8) → Cook with long division → Serve 0.375 on plate

Recall Trigger

Start your house journey at the front door with a fraction

Tags

• process
• rule

Topic

Rounding Decimals

Concept

Rounding Decimals

Anchor Id

A12

Difficulty

easy

Memory Aid

The Digit Detective Story: You're a detective looking at the digit in the rounding place. Look to your right at the next digit - this is your witness. If the witness is 5 or more, they're telling the truth, so round UP (add 1 to your digit). If the witness is 4 or less, they're lying, so round DOWN (keep your digit the same). All digits to the right of your rounding place disappear - they've left the scene!

Anchor Type

micro_story

Why It Works

Detective story makes the decision-making process memorable and logical

Example Usage

Round 3.247 to nearest tenth: Detective looks at 2 (tenths), witness 4 is lying, so keep 2. Answer: 3.2

Recall Trigger

Picture yourself as a detective questioning digit witnesses

Tags

• properties
• sequence

Topic

Properties of Real Numbers

Concept

Properties of Real Numbers

Anchor Id

A13

Difficulty

hard

Memory Aid

ADAM DI CA: Associative, Distributive, Additive identity, Multiplicative identity, Distributive, Identity, Commutative, Additive inverse. Like remembering the names of your barkada members for group work assignments!

Anchor Type

acronym

Why It Works

Creates a memorable name-like acronym that sounds Filipino

Example Usage

When asked about properties, recall ADAM DI CA and expand: A=Associative (grouping), D=Distributive, etc.

Recall Trigger

Think of your friend ADAM DI CA joining your study group

Tags

• process
• visual

Topic

Prime Factorization

Concept

Prime Factorization Process

Anchor Id

A14

Difficulty

medium

Memory Aid

Build a family tree, but for numbers! Start with the big kuya (original number) at the top. He has two anak (factors) below him. Keep splitting each anak until you reach the bunso (prime numbers) who can't be split anymore. These bunso are your prime factors - the youngest generation of the number family.

Anchor Type

visual_association

Why It Works

Filipino family structure provides familiar hierarchical framework

Example Usage

For 60: Kuya 60 has anak 6 and 10, 6 splits to bunso 2 and 3, 10 splits to bunso 2 and 5. Prime factors: 2, 2, 3, 5

Recall Trigger

Picture a family tree with kuya at top, bunso at bottom

Tags

• comparison
• process

Topic

Comparing Fractions

Concept

Comparing Fractions

Anchor Id

A15

Difficulty

medium

Memory Aid

Comparing fractions is like comparing heights of students from different classes. You can't directly compare unless they're standing on the same floor level (common denominator). Cross multiplication is like using a measuring tape that works across different floors - multiply the numerator of each fraction by the denominator of the other to get comparable measurements.

Anchor Type

analogy

Why It Works

Height comparison is intuitive, and the measuring tape analogy explains cross multiplication

Example Usage

Compare ³⁄₄ vs ²⁄₃: Cross multiply (3×3=9, 4×2=8). Since 9>8, we have ³⁄₄ > ²⁄₃

Recall Trigger

Picture students on different floors needing a measuring tape

Tags

• definition
• concept

Topic

Absolute Value

Concept

Absolute Value

Anchor Id

A16

Difficulty

easy

Memory Aid

The Security Guard Story: Absolute value bars | | are like security guards at a mall entrance. No matter which direction you come from (positive or negative), the security guard only cares about your distance from the entrance (zero). If you're 5 steps to the left (-5) or 5 steps to the right (+5), the guard records your distance as simply 5 steps.

Anchor Type

micro_story

Why It Works

Familiar mall security scenario makes the distance-from-zero concept clear

Example Usage

For |-7|: Security guard sees you're 7 steps away from entrance (zero), records distance as 7

Recall Trigger

Picture security guards measuring distance from mall entrance

Tags

• rule
• process

Topic

Divisibility Rules

Concept

Divisibility by 6

Anchor Id

A17

Difficulty

medium

Memory Aid

6 = 2×3 Marriage: For a number to be divisible by 6, it must be 'married' to both 2 and 3. Like a Filipino wedding, both families (2 and 3) must approve! Check: Is it even? (divisible by 2) AND Do digits sum to multiple of 3? Both must say 'Oo' for the marriage to happen!

Anchor Type

chunking

Why It Works

Marriage metaphor makes the 'both conditions must be met' rule memorable

Example Usage

For 42: Even? Yes (family 2 approves). Digit sum 4+2=6, divisible by 3? Yes (family 3 approves). Wedding approved - 42÷6 = 7!

Recall Trigger

Think of a wedding where both families must approve

Tags

• classification
• hierarchy

Topic

Number System

Concept

Number System Hierarchy

Anchor Id

A18

Difficulty

hard

Memory Aid

Picture the Philippine archipelago: Natural numbers are like main islands (1,2,3...), Whole numbers add the surrounding water (includes 0), Integers add the ocean depths (negative numbers), Rational numbers add all the boats and ships (fractions), Irrational numbers are the mysterious sea creatures (π, √2), Real numbers include everything in our ocean world, and Complex numbers add the sky above (imaginary).

Anchor Type

visual_association

Why It Works

Uses familiar geographic metaphor to show expanding number system

Example Usage

When classifying -3/4: It's in the rational ocean (fraction), which includes the integer depths and natural islands

Recall Trigger

Picture the Philippine islands expanding to include ocean and sky

Formula

LCM × GCF = Product of the two numbers

Mnemonic

Love Conquers Great Fear - Product! Picture lovers (LCM and GCF) whose love multiplied equals the product of their family numbers. The stronger their love bond, the more their families are connected!

When To Use

To verify your LCM and GCF calculations, or to find one when you know the other

What Each Part Means

LCM (Least Common Multiple) × GCF (Greatest Common Factor) always equals the product of the original two numbers

Formula

Mixed number to improper: (whole × denominator) + numerator / denominator

Mnemonic

MAD formula: Multiply, Add, Drop! Basketball player (whole) × court sections (denominator) + balls held (numerator), all over court sections (denominator)

When To Use

Converting mixed numbers to improper fractions for easier calculation

What Each Part Means

Whole number multiplied by denominator, plus the existing numerator, all over the same denominator

Formula

Cross multiplication for comparing fractions: a/b vs c/d → compare a×d vs b×c

Mnemonic

X marks the spot! Draw an X across the fractions - multiply along each arm of the X to compare. Like treasure hunting where X shows you the way!

When To Use

Comparing fractions with different denominators

What Each Part Means

Multiply numerator of first fraction by denominator of second, compare to numerator of second by denominator of first

Formula

a/b ÷ c/d = a/b × d/c

Mnemonic

Keep Change Flip (KCF): Keep the first fraction, Change division to multiplication, Flip the second fraction. Like driving - Keep your lane, Change gears, Flip your turn signal!

When To Use

Dividing fractions

What Each Part Means

Division by a fraction equals multiplication by its reciprocal

Formula

Prime factorization method for GCF: multiply common prime factors with lowest powers

Mnemonic

Common Ground Minimum Power: Take only the common prime factors and use the minimum power each appears. Like sharing - take only what everyone has, in the smallest amount anyone has!

When To Use

Finding GCF using prime factorization

What Each Part Means

Find prime factors that appear in all numbers, use the lowest exponent for each common factor

Formula

Prime factorization method for LCM: multiply all prime factors with highest powers

Mnemonic

All Maximum Power: Take ALL prime factors from all numbers, use the maximum power each appears. Like party planning - bring everything anyone mentioned, in the largest quantity anyone suggested!

When To Use

Finding LCM using prime factorization

What Each Part Means

Include every prime factor that appears in any number, using the highest exponent for each factor

Chain Title

PEMDAS Order of Operations

Recall Test

What operation comes after exponents in 2 + 3 × 4²?

Memory Chain

Please Excuse My Dear Aunt Sally - Picture your tita serving a traditional meal in perfect order: bowls (parentheses) first, extra rice piled high (exponents), portions multiplied and divided fairly, then final additions and subtractions of condiments

Items To Remember

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

Chain Title

Steps to Check if Number is Prime

Recall Test

What's the first step to check if 97 is prime?

Memory Chain

Square Root Detective Agency: First FIND the square root boundary, LIST all prime suspects, TEST each suspect as potential factor, IF none work, declare the number PRIME and close the case!

Items To Remember

• Find square root
• List prime numbers up to square root
• Test each prime as factor
• If no factors found, number is prime

Chain Title

Converting Fractions to Decimals

Recall Test

After setting up division for ⅜, what's the next step?

Memory Chain

Kitchen Division Recipe: SET up your ingredients (division), DIVIDE the main ingredient (numerator) by servings (denominator), ADD the decimal seasoning, CONTINUE cooking until done, IDENTIFY if it's a complete dish (terminating) or needs repeating!

Items To Remember

• Set up division
• Divide numerator by denominator
• Add decimal point
• Continue dividing
• Identify terminating or repeating

Chain Title

Prime Factorization Steps

Recall Test

After finding two factors of a number, what should you check next?

Memory Chain

Family Tree Building: START with the family patriarch (number), FIND his two children (factors), CHECK if children can have kids (composite) or are bunso (prime), CONTINUE building branches for composite children, LIST all the bunso (prime factors) at the bottom

Items To Remember

• Start with the number
• Find two factors
• Check if factors are prime
• Continue factoring composite factors
• List all prime factors

Chain Title

Adding Fractions with Different Denominators

Recall Test

After finding the LCD for ¼ + ⅓, what's the next step?

Memory Chain

Sari-sari Store Merger: FIND common container size (LCD), CONVERT all portions to same container, ADD the portions together, KEEP using the same container size, SIMPLIFY by using smaller containers if possible

Items To Remember

• Find LCD
• Convert fractions
• Add numerators
• Keep same denominator
• Simplify if needed